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Cryptographic method with elliptical curves

An elliptic curve and cryptography technology, which is applied in the calculation using non-number system, calculation using residual algorithm, input/output of user/computer interaction, etc. It can solve problems such as non-check and attack.

Active Publication Date: 2013-03-06
SIEMENS AG
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, in this method there is no check whether the points are really elements of the elliptic curve
[0014] The resulting possibility is that a side-channel attack

Method used

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  • Cryptographic method with elliptical curves
  • Cryptographic method with elliptical curves
  • Cryptographic method with elliptical curves

Examples

Experimental program
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Embodiment Construction

[0082] exist figure 1 A flow chart is shown in , which illustrates an embodiment of the method according to the invention. In a first step, a library with an elliptic curve E is provided (S1). The elliptic curve E is defined by a finite ontology K. Thus, the curve E contains a finite number of points P. As already described, elliptic curves pass through the Weierstrass equation with the parameter a 1 、a 2 、a 3 、a 4 and a 6 to make sure. Individual parameters can be zero by limiting or changing the parameterization accordingly. The parameters are chosen such that the elliptic curve is not singular.

[0083] The order of the elliptic curve is then determined (S2). The order of the elliptic curve is understood to be the number of points on the body K which satisfy the Weierstrass equation. Geometrically, this is all points P lying on the elliptic curve E.

[0084] The order of the elliptic curve (abbreviated ord(E)) should be a prime number. If the check reveals that...

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PUM

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Abstract

A method determines an elliptical curve, suitable for a cryptographic method. An elliptical curve to be tested is prepared. The order of a twisted elliptical curve associated with the elliptical curve to be tested is determined. It is automatically checked whether the order of the twisted elliptical curve is a strong prime number. If the order of the twisted elliptical curve is a strong prime number, the elliptical curve to be tested is selected as an elliptical curve suitable for cryptographical methods.

Description

technical field [0001] The invention relates to a method for determining elliptic curves, in particular elliptic curves suitable for cryptographic data processing. Furthermore, the invention relates to a cryptographic method and a device which are based on preselected elliptic curves. Background technique [0002] Cryptographic methods are used inter alia for encrypting messages, signing documents and authenticating persons or objects. So-called asymmetric encryption methods are particularly suitable for this, which provide private and secretly kept keys and public keys for the user. [0003] When encrypting a message, the sender tries to obtain the public key of the intended recipient and encrypts the message with it. Only the recipient can then decrypt the message using a private key known only to him. [0004] When signing a document, the signer uses his private key to calculate an electronic signature from the document. Others can verify the signature with the help o...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F7/72
CPCG06F7/725G06F2207/7219G06F3/03G06F7/72G06F21/00
Inventor J·乔治亚德斯A·卡格尔B·迈耶
Owner SIEMENS AG